Transport Modeling

Alok Jain
Kowloon Canton Railway Corporation
 Overview:
Basic Modeling Framework

• Data collection
• Mathematical Modeling
• Calibration/Validation
• Future Forecasts
 Overview: The Basic Premise
• Degree of detail required
– Zonal definitions
– Network definitions
– Modal definitions
• Purpose of the model
– Strategic vs. Local area modeling
– Infrastructure Planning vs. Management
– Highway or Public Transport
– Passenger vs. Freight
 A Simple Supply-Demand Model

• A linear supply-demand model

1. Qd = a + b*p Qd = Quantity demanded
2. Qs = c + d*p Qs = Quantity supplied

 At equilibrium, Qd = Qs = q p = Price

∴ a + b*p = c + d*p Endogenous variable: p, q

⇒ p = (a – c) / (d – b) Parameters: a, b, c, d
 Replacing p in 1, we get
⇒ q = (ad – bc) / (d – b)
A Simple Supply-Demand Model

b < 0 & d > 0: slope

a > 0: intercept
c < a: zero price principle
 Classic 4-stage Transport Model

• Trip Generation/Attraction Land Use Forecast

• Trip Distribution
Planning
• Modal Split Generation
Inputs
• Assignment
Trips by
N Distribution
OD zones
E
T
Trips by
W Modal Split
Mode
O
R
K Assignment Link Flows
 Trip Generation/Attraction

Ti = f ( Si ) Ti = Traffic Generated by zone i

and Tj = Traffic Attracted to zone j

Tj = f ( Sj ) Si & Sj = Socio-economic and/or land use variable

• Car ownership, family size, household size,
length of residence, family income, age
distribution, driving license, distance from
CBD, occupation, house type etc.
• Offices, Industry, Commerce, Shops,
Education & health, Public buildings, Open
Space, Transport & utilities, vacant land
 Trip Distribution

• Trip distribution is often modeled in the

form of a trip matrix
Attractions
Generations 1 2 3 ..j ..z Σ Tij

1 T11 T12 T13 T1j T1z O1

2 T21 T22 T23 T2j T2z O2
3 T31 T32 T33 T3j T3z O3
i Ti1 Ti2 Ti3 Tij Tiz Oi
z Tz1 Tz2 Tz3 Tzj Tzz Oz
Σ Tij D1 D2 D3 Dj Dz Σ Tij=T
 Trip Distribution

Typical Form Fij = Impedance to travel between i & j

Tij = f ( Ti , Tj , Fij ) • Can be represented by travel
distance, time, costs or a combination
of them

Gravity Model k = constant to scale the estimate up/down

Tjj = k Ti Tj / ( Fij )n n = constant to permit the manipulation of
friction (usually 1<n<2)
 Trip Distribution

• Travel between two zones depend on

– the relative attractiveness of each area,
– the distance between each area
– the generalised cost of accessing each area
(time taken in-vehicle, time taken waiting and
interchanging)
 Generalized Cost
• Usually represented as a linear function of journey attributes
weighted by coefficients attempting to represent the relative
importance as perceived by the traveller.

Cij = a1tvij + a2twij +a3ttij + a4tnij + a5Fij + a6mj + p

tvij = in vehicle travel time between i and j
twij = walking time to and from stops (stations)
ttij = waiting time at stops
tnij = interchange time (if any)
Fij = the fare between i and j
m = terminal cost for making the journey between i and j (e.g.parking cost)
p = modal penalty ( a parameter representing all other attributes not so far
represented, e.g. comfort, safety, convenience)
 Modal Split

• Division of journeys (trips) between modes

• Mode split often confined to public & private
transport
– Choice riders vs. captive riders
 Passenger Modal Split
• Depends on 5 general categories of influential factors
1. Characteristics of the Trip
• Length of Trip
• Trip Purpose
• Destination
• Access to Place of Departure
2. Characteristics of the Mode
• Comfort
• Reliability
• Safety (or perception of safety)
• Timetable
• Other factors such as ease of booking, catering facilities, toilet
facilities, comfort of terminals etc.
 Passenger Modal Split
3. Characteristics of the Household.
• Income (or affordability)
• Car Ownership
• Size and Composition of Household (old, young, disabled people more
likely to use public transport than private transport)
• Occupation (White collar workers more likely to use private transport)

4. Zonal Characteristics
• Residential Density (more public transport at high residential density)
• Concentration of Workers
• Distance from Central Business District (CBD)
 Passenger Modal Split
5. Network Characteristics
• Accessibility Ratio (measure of the relative accessibility of one zone to
all other zones by means of public transport and the road network)
• Travel Time Ratio (measure of the time taken to travel to a destination
by public transport relative to the private transport. The total travel
time by public transport consists of:
– Walking time to terminal at origin + waiting time + in-vehicle time +
walking time to destination
Travel time by private transport consists of:
– driving time + parking time + walking time from parking to destination
As the travel time ratio increases, usage of public transport decreases)
• Travel Cost Ratio (measure of the money cost of travelling by public
transport compared to private transport. As the ratio increases, public
transport will be used less)
 Freight Modal Split

• Depends on four general categories

1. Characteristics of the Goods to be Transported
• Quantity of Goods to be Carried
• Type of Goods to be Transported
• Security of Goods
2. Characteristics of the Trip
• Distance
• Speed
 Freight Modal Split
• Depends on four general categories
3. Characteristics of the Mode
• Reliability
• Customer Service
• Control
• Flexibility
• Availability (time lag between the recognition that transport is
required and actually obtaining the transport)
4. Characteristics of the Network
• Transport Cost Ratio (measure of the money cost of sending goods by
one form of transport compared to another)
• Travel Time Ratio
• Accessibility
 Modal Split Model

Typical Form Iijm = represents the attributes of

various competing modes
Tijm = f ( Iij1 ,…., Iijm , Tij )
 Modal Split Model

• Application of behavioral models

– Derived from micro-economic theory of consumer
behavior and utility maximization
– Revealed preference & stated preference
– Random utility and multinomial logit models
 Assignment
Typical Form
Tijmp = f ( Iijm1 ,…., Iijmp , Tijm )

• All-or-nothing assignment
– Least-cost route but assumes zero flow & perfect information
• Multiple path assignment
– Assumes that, in a congested situation, traffic would be spread
over all alternative routes in a way that travel costs become
equal
– Results in equilibrium (no individual can improve utility by
finding a less costly route)
 Behavioral Travel Demand Model

• A vast array of factors affect mode choice

decisions
• Market demand/supply curve is obtained from
aggregating all individual decisions on mode
choice
• Application of behavioral models
– Derived from micro-economic theory of consumer
behavior and utility maximization
 Behavioral Travel Demand Model

• Driving factors:
– Individual decision-making behaviour is the root cause
of market demand (why instead of what)
– Large chunks of microeconomic theory already relate
to the behaviour of individuals
– Survey data relating to individuals and households is
becoming more and more available – improved
accuracy
 Modeling assumptions
• Decision-maker: who is the decision-maker, and
what are his/her characteristics;
• Alternatives: possible options of decision-maker;
• Attributes: of each potential alternative that the
decision-maker is taking into account to make his/
her decision;
• Decision rules: the process used by the decision-
maker to reach his/her choice.
 1. Decision Maker
• When group is the decision-maker, we ignore all
internal decisions within the group, and consider only
the decision of the group as a whole
• Selection of attributes must be those likely to explain
the choice of the individual.
– No automatic process to perform this identification. The
knowledge of the actual application and the data availability
play an important role in this process.
 2. Alternatives
• What has been chosen, but also what has not been
chosen.
• The set containing the alternatives, called the
choice set, must be characterized on the context of
the application.
• Discrete choice set: contains a finite number of alternatives
that can be explicitly listed. The corresponding choice
models are called discrete choice models.
• The choice of a transportation mode is a typical application
leading to a discrete choice set.
 2. Choice Set Conditions
• At least two alternatives from which a choice must be made.
• Number of alternative choices in the choice set must be finite.
– It must be possible to identify all possible courses of action.
• The available choices must be mutually exclusive.
– If one alternatives is chosen, then all other alternatives in the choice set
must not be chosen i.e., it must be impossible to make more than one of
the available choices at any decision point e.g. for analysing a
commuter's trip to work, some combination of bus and train might be
possible and this should be included in the choice set as one possibility.
• The set of alternatives must be exhaustive.
– All possible alternative choices must be identified and form part of the
choice set
 3. Attributes
• Attributes of each alternatives that are likely to affect the choice
of the individual.
– for car list could include travel time, out-of-pocket cost and comfort
– list for bus could include travel time, out-of-pocket cost, comfort and bus
frequency
• Some attributes are generic to all alternatives, and some may be
specific to an alternative
• An attribute can be a function of available data, not necessarily a
directly observed quantity
– The out-of-pocket cost may be replaced by the ratio between the out-of-
pocket cost and the income of the individual
 4. Decision Rules

• Rules used by the decision-maker to come up

with the actual choice
• Different sets of assumptions lead to different
family of models
– The neoclassical economic theory, based on the
concept of utility
– The random utility models are designed to capture
uncertainty
 Random Utility Models

• RUMs are based on the deterministic decision rules, where

uncertainty is captured by random variables representing utilities
• RUMs assume that decision-maker has perfect discrimination
capability
• But the analyst is supposed to have incomplete information and,
therefore, uncertainty must be taken into account. Four different
sources of uncertainty:
– unobserved alternative attributes
– unobserved individual attributes
– measurement errors and
– proxy, or instrumental variables
 Random Utility Models

• The utility is modeled as a random variable in order to reflect

this uncertainty. More specifically, the utility that individual i
is associating with alternative a is given by

– where Vai is the deterministic part of the utility, and εai is the
stochastic part, capturing the uncertainty
• The alternative with the highest utility is supposed to be
chosen. Therefore, the probability that alternative a is chosen
by decision-maker i within choice set C is
 Logit (Logistic Probability Unit) Models

• Most widely used

• A different decision maker in exactly the same
position as the first, faced with exactly the same set
of characteristics for each of the alternatives, may
well make a different decision because he/she could
attach different weights to the characteristics upon
which the alternatives are being judged.
 Logit (Logistic Probability Unit) Models

• Employing utility theory, the decision maker will

choose the alternative which maximises their utility
(happiness, satisfaction, pleasure).
• The amount of utility that is derived from each of the
alternatives depends on the characteristics of the
choice and the characteristics of the decision maker.
• Defining the probability of selecting a particular
choice, it must either be 0 if it yields less utility or it
must be 1 if it yields more utility.
 Logit (Logistic Probability Unit) Models

• Therefore, the predictions which the logit model produces for

a specific mode choice decision cannot be 100% certain. There
is a certain probability that the prediction is correct.
• This implies that if the same individual faced this same choice
a number of times, the predicted mode choice will be correct
for a certain proportion of the choice situations. This
proportion would correspond to the probability of an accurate
prediction.
 Logit (Logistic Probability Unit) Models

U in
e
Pin =
∑ej
U jn

• where:
• Pin = the probability that individual n chooses choice i
• Uin = the utility that individual n derives from choice i
• Ujn = the utility that individual n derives from all j
choices in the choice set
 Logit (Logistic Probability Unit) Models

1. Each of the choice probabilities falls between zero and unity.

• If a particular choice alternative had a very low utility then the
probability of it being selected as the preferred mode is extremely low
(ie. Pin approaches zero). On the other hand, a mode choice with a
high level of utility would be very likely to be selected as the
preferred mode choice (Pin approaches unity).
2. The sum of all the choice probabilities must sum to one.
3. The relationship between the probability of selecting a
particular mode and the level of utility which it provides
should be sigmoid in shape
 Logit (Logistic Probability Unit) Models
• If the utility of one alternative is very
low compared to other alternatives,
then a small increase in the level of
that utility should not have too drastic
an impact on the probability of the
preferred alternative and vice versa.
• A change in the level of utility of one
option has the greatest effect when its
utility is very similar to that of other
options. In this case, a small
improvement in the level of utility in
one mode, for example, may well tip
the balance in favour of that mode
compared to other alternatives and
lead to a large increase in the
probability of it being selected.
 Advanced Logit Models

• Hierarchical Logit Models

• A decision tree approach
• Nested Logit Models
– Transit models
 Land Use Factors affecting Travel

• Density & Clustering

– Land use accessibility
– Transportation Choice
– Space-saving modes
– Land-use mix
• Higher density and clustering tend to
reduce car ownership and usage
Land Use Factors affecting Travel
Land Use Transport Interaction
 Land Use Transport Modeling (LUTM)

• Urban simulation is a unique modelling problem

– Urban models – economic, social and environmental -
are difficult to simulate
– Profound influences upon people’s lives
– Policies and ideas difficult to experiment with
• Earlier, transport modeling treated land use
variables as exogenous
• Now, the feedback to land use pattern is explicitly
recognized
General Structure of LUTM
THANK YOU